detl ============================================== Purpose ---------------- Returns the determinant of the last matrix that was passed to one of the intrinsic matrix decomposition routines. Format ---------------- .. function:: y = detl() Examples ---------------- If both the inverse and the determinant of the matrix are needed, the following two commands will return both with the minimum amount of computation: :: xi = inv(x); xd = detl; The function :func:`det(x)` returns the determinant of a matrix using the Crout decomposition. If you only want the determinant of a positive definite matrix, the following code will be the fastest for matrices larger than 10x10: :: /* ** The 'call' keyword tells GAUSS to ignore the values ** returned from chol */ call chol(x); xd = detl; The Cholesky decomposition is computed and the result from that is discarded. The determinant saved during that instruction is retrieved using :func:`detl`. This can execute up to 2.5 times faster than :func:`det(x)` for large positive definite matrices. Remarks ------- Whenever one of the intrinsic matrix decomposition routines is executed, the determinant of the matrix is also computed and stored in a system variable. This function will return the value of that determinant and, because the value has been computed in a previous instruction, this will require no computation. The following functions will set the system variable used by :func:`detl`: +-------------------------+-----------------------------------------------------+ | :code:`chol(x)` |   | +-------------------------+-----------------------------------------------------+ | :code:`crout(x)` |   | +-------------------------+-----------------------------------------------------+ | :code:`croutp(x)` |   | +-------------------------+-----------------------------------------------------+ | :code:`det(x)` |   | +-------------------------+-----------------------------------------------------+ | :code:`inv(x)` |   | +-------------------------+-----------------------------------------------------+ | :code:`invpd(x)` |   | +-------------------------+-----------------------------------------------------+ | :code:`solpd(y, x)` | determinant of x | +-------------------------+-----------------------------------------------------+ .. seealso:: Functions :func:`det`, :func:`norm`